This invention relates to a devices and methods for trisecting an angle.
Various devices have been proposed to enable trisecting of angle. Most are complex, comparatively expensive, difficult to use or suffer some significant shortcoming, as will be apparent from the prior art references below.
U.S. Pat. No. 1,145,369 to Kaplan describes a device that relies on a pair of external limiting members pivotally connected to each other with complex links. The mechanism is cumbersome and relatively expensive.
U.S. Pat. No. 1,764,581 to Shibuya describes angle trisector that uses a modified protractor. The device is potentially inexpensive to produce but the user must select proper graduations and perform calculations, making use complex.
U.S. Pat. No. 2,222,853 to Neurohr describes an angle trisector which uses a pair of side arms and a set of bars or arms pivotally connected to the side arms. The device is relatively expensive to produce and cumbersome to use or transport.
German disclosure No. 1611808, published on Feb. 13, 1968, describes a template for trisecting an angle. The template has a central horizontal line and five holes equally spaced along the line by a distance r. The center hole serves as the center of a circle of radius r. The periphery of the template is defined by two intersecting circles of radius 2r centered about the outermost holes. When the periphery is properly centered within angle, a pair of hypothetical lines through the vertex and tangential to the circle effectively trisect the angle. Although potentially inexpensive, a major shortcoming is that the two trisecting lines cannot be drawn or readily marked for drawing.
Russian Patent No. SU1735061-A1 to Memyrin describes a mechanism comprising cranks and slides linked to trisect an angle. The mechanism is complex, expensive and cumbersome.
U.S. Pat. No. 5,210,951 to Chen describes an instrument for trisecting an angle that has two circular planes and four pointers. Two pointers are intended to define either an acute or obtuse angle. Two other pointers are intended to divide the angle into three equal angles when oriented perpendicular to one other. The device is relatively expensive but awkward to use.
In general, the invention provides a template that in effect identifies three congruent triangles between an angle to be trisected. The template relies on aligning and marking points (preferably defined by simple clearance holes) and a circular arc, all observing specific geometric relationships. This arrangement allows the template to be positioned to mark trisecting lines, effectively along certain sides of the hypothetical triangles. This operating principle need not be understood to use the template but will be described in greater detail below with reference to the drawings.
In one aspect, the invention provides a template for trisecting an angle displayed on a flat surface. The template comprises a first aligning point adapted for visual location over one arm of the angle, a second point where a marking hole is located, a line intended to be placed into intersecting relationship with the vertex of the angle, and a circular arc intended to be aligned in tangential relationship with the other arm of the angle. The line is perpendicular to a hypothetical line between the first and second points and aligned axially with the midpoint of the hypothetical line. The circular arc adapted for visual location in tangential relationship with the other arm. The circular arc is centered about the second point and has a radius equal to one half of the distance between the first and second points.
In one embodiment, the invention provides a transparent angle-trisecting template that comprises a pair of clearance holes, and a pair of circles of equal radius, each centered about a different clearance holes. The circles have a radius equal to one-half of the distance between the clearance holes, and consequently side-by-side forming a point contact. A central clearance hole is located at the midpoint of a hypothetical line between the pair of clearance holes, substantially at the point of contact between the two circles. A line extends perpendicular to the hypothetical line in aligned with the midpoint of the hypothetical line. This embodiment is symmetric and gives the user the option of using either circle to orient the template against one arm of the angle. The central clearance hole of the other circle can be located over the other arm. In this embodiment, the peripheral shape of the template is immaterial.
In another embodiment, the invention provides a template whose periphery is instrumental to trisecting an angle. The template comprises a pair of clearance holes, a lateral side edge perpendicular to a hypothetical line between the clearance holes and aligned with the midpoint of the line, and a projection that extends laterally relative to the side edge. The projection has a part-circular periphery centered about one of the clearance holes and has a radius equal to one-half the distance between the clearance holes. The template is positioned relative to an angle in substantially the same manner as discussed above. However, once oriented, the lateral side edge can be used to immediately draw one trisecting line. The other trisecting line is marked through the clearance hole centered in the part-circular periphery, and can be drawn with a straight edge extended through the vertex of the angle to the mark.
Other aspects of the invention will be apparent from a description below of preferred embodiments and will be more specifically defined in the appended claims.